Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs

We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in graph theory.

Automated summary

The paper explores the survival probability of Grover walks with sinks and their connection to Grover walks with tails, showing that the relationship between them can be described using eigenspaces.